Poissonian Behavior of Ising Spin Systems in an External Field
نویسندگان
چکیده
We apply the Stein-Chen method for Poisson approximation to spin-half Isingtype models, in positive external eld, which satisfy the FKG inequality. In particular we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is inversely proportional to the number of lattice sites (we obtain upper and lower bounds on the total variation distance between the exact distribution and its Poisson approximation). We illustrate these results by application to speci c models, including the meaneld and nearest-neighbour ferromagnetic Ising models.
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